The insect celestial compass has been studied extensively in the honeybee Apis mellifera, the cricket Gryllus campestris, the locust Schistocerca gregaria, the monarch butterfly Danaus plexippus, the dung beetle Scarabaeus lamarcki and the desert ant Cataglyphis bicolor. Angular distances above 90° have decreasing degree of linear polarisation. From the point of view of an earth based observer, as the angular distance from the sun increases from 0° to 90°, the degree of linear polarisation in skylight increases, with the principal axis of polarisation perpendicular to the observer-sun axis, forming concentric rings around the sun. As light from the sun passes through earth’s atmosphere it undergoes a scattering process producing differing levels of polarisation across the sky-dome relative to the position of the sun. Linear polarisation of light is the alignment of orientation of oscillation of the electromagnetic wave to a single plane. The position of the sun (or moon) in the sky - as well as providing a direct directional reference point - determines the properties of light across the skydome including intensity and chromatic gradients, and a specific pattern of polarisation. The primary directional cue used for path integration by central place foraging insects such as desert ants is the sky (sometimes called the celestial compass). Our main aim in this paper is to study the potential accuracy with which an insect can estimate its allocentric direction from the sky polarisation pattern, given realistic constraints on the environmental cues, the sensory system, and the various sources of disturbances. In a habitat with few if any landmarks, these ants can integrate the distance and directions travelled on a tortuous search path of up to a kilometre in length and make a direct return home when food is found. The benefit of such accurate external compass systems is exemplified in the behaviour of desert ants, who utilise the sky polarisation pattern. To avoid this limitation, many animals, in particular insects, have developed an array of sensory systems to detect allothetic directional cues in their environments: magnetic (butterflies, moths, ants ), wind (moths, ants ), and visual, crickets, locusts, butterflies, ants, dung beetles ) star compass - (dung beetle )]. Idiothetic cues such as those generated in the mammalian vestibular system are useful for short time periods but are inherently problematic because of accumulating errors. Orientation cues are required for spatial behaviours from following a straight line to migrating across continents (for a theoretical proof see ).
We discuss the plausibility of our model to be mapped to known neural circuits, and to be implemented for robot navigation. We demonstrate that the compass is robust to disturbances and can be effectively used as input to an existing neural model of insect path integration.
We also show that the confidence can be used to approximate the change in sun position over time, allowing the compass to remain fixed with respect to ‘true north’ during long excursions.
We introduce a method to correct for tilting of the sensor array, as might be caused by travel over uneven terrain. By processing the degree of polarisation in different directions for different parts of the sky, our model can directly estimate the solar azimuth and also infer the confidence of the estimate.
Here we examine how such compass information could be reliably computed by the insect brain, given realistic constraints on the sky polarisation pattern and the insect eye sensor array. Fundamental to the reliability of this process is the use of a neural compass based on external celestial cues. Many insects navigate by integrating the distances and directions travelled on an outward path, allowing direct return to the starting point.
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